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Chapter 4: Problem 40

Express answers in standard notation. $$ \frac{400,000 \times 0.05}{0.008 \times 25,000} $$

Short Answer

Expert verified
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Step by step solution

01

Simplify the expression

First, rewrite the given expression: \(\frac{400,000 \times 0.05}{0.008 \times 25,000}\)
02

Calculate the numerator

Compute the product in the numerator: \(400,000 \times 0.05 = 20,000\)
03

Calculate the denominator

Compute the product in the denominator: \(0.008 \times 25,000 = 200\)
04

Divide the simplified numbers

Divide the simplified numerator by the simplified denominator: \(\frac{20,000}{200} = 100\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator
In math, the numerator is the top number of a fraction. It shows how many parts of a whole we have. In the given exercise, the numerator is the expression on top of the fraction: \(400,000 \times 0.05\). This part of the problem tells us what needs to be divided by the denominator.

To solve, we first simplify the numerator: \(400,000 \times 0.05 = 20,000\). Multiplying these numbers might look tricky, but remember, multiplying by 0.05 is the same as finding 5% of 400,000.

Tips for handling numerators:
  • Make sure to correctly follow the arithmetic operations.
  • Check for any common factors if simplifying fractions further.
Denominator
The denominator is the bottom number of a fraction. It shows into how many parts the whole is divided. In the exercise, the denominator is \(0.008 \times 25,000\). This part will tell us by how much we need to divide the numerator.

To solve, we simplify this expression: \(0.008 \times 25,000 = 200\). Here, multiplying by 0.008 means finding 0.8% of 25,000, answering how we split up the numerator.

Tips for handling denominators:
  • Always check to carry out the correct operations.
  • Simplify whenever possible to make calculations easier.
Simplification
Simplification means making a mathematical expression easier to understand and work with. In fractions, we simplify by following exact arithmetic steps to reduce expressions.

For this exercise, after calculating both the numerator (20,000) and the denominator (200), we divide them: \(\frac{20,000}{200} = 100\). This division leaves us with an answer in its simplest form.

Simplification tips:
  • Break down the steps into smaller, manageable parts.
  • Double-check each step to avoid mistakes.
  • Ensure that every part of the fraction, both numerator and denominator, are simplified before dividing.

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Most popular questions from this chapter

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